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COMPLEX TIME: Adaptation, Aging, & Arrow of Time

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Irreversible Processes in Ecological Evolution

From Complex Time

Category: Application Area Application Area: Ecology

Date/Time: January 29, 2019 - January 31, 2019

Location: Santa Fe Institute (Noyce Conference Room)

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  • Jacopo Grilli (ICTP)

  • Dervis Can Vural (Univ. Notre Dame)

  • Meeting Highlight

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    Click each agenda item's title for more information.
    Tuesday, January 29, 2019
    8:15 am - 8:45 am Day 1 Continental Breakfast (outside SFI Noyce Conference Room)
    8:45 am - 9:15 am Welcome & introduction around the room - Jacopo Grilli (ICTP), Dervis Can Vural (Univ. Notre Dame)
    9:15 am - 9:30 am Working Group Context Framing - Jacopo Grilli (ICTP) Download Presentation
    9:30 am - 10:00 am WG Context under Adaptation, Aging, Arrow of Time project - Amy P Chen (SFI), David Krakauer (SFI) Download Presentation
    10:00 am - 11:00 am Pathogen diversity and negative frequency-dependent selection: consequences for intervention - Pamela Martinez (Harvard) Download Presentation
    11:15 am - 12:15 pm Emergent structure and dynamics in stochastic, open, competitive communities - Annette Ostling (Univ. Michigan) Download Presentation (Encrypted)
    12:15 pm - 12:45 pm Open discussion & reflection time I
    12:45 pm - 1:30 pm Day 1 Lunch (outside SFI Noyce Conference Room)
    1:30 pm - 2:30 pm Natural selection, population cycles, and climate change in forest insects - Greg Dwyer (Univ. Chicago) Download Presentation
    2:30 pm - 3:30 pm Cooperative growth and cell-cell aggregation in marine bacteria - Otto Cordero (MIT)
    3:30 pm - 3:45 pm Day 1 PM Break
    3:45 pm - 4:45 pm Statistical mechanics of microbiomes - Robert Marsland (Boston Univ.) Download Presentation (Encrypted)
    4:45 pm - 5:15 pm Open discussion & reflection time II
    Wednesday, January 30, 2019
    8:15 am - 8:45 am Day 2 Continental Breakfast (outside SFI Noyce Conference Room)
    8:45 am - 9:45 am Phenotypic evolution in the Anthropocene - Priyanga Amarasekare (UCLA) Download Presentation
    9:45 am - 10:45 am Irreversible processes in ecological networks - Fernanda Valdovinos (Univ. Michigan) Download Presentation
    10:45 am - 11:00 am Day 2 AM Break
    11:00 am - 12:00 pm Are changes in species interactions and their ecosystem consequences irreversible? - Samraat Pawar (Imperial College London) Download Presentation (Encrypted)
    12:00 pm - 12:30 pm Open discussion & reflection time III
    12:30 pm - 1:30 pm Day 2 Lunch (outside SFI Noyce Conference Room)
    1:30 pm - 2:30 pm Higher-order interactions, stability across timescales, and macroecological patterns - Jacopo Grilli (ICTP) Download Presentation
    2:30 pm - 3:30 pm Population genetics of low-probability transitions - Stephen Proulx (UCSB) Download Presentation
    3:30 pm - 3:45 pm Day 2 PM Break
    3:45 pm - 4:15 pm Day 2 Reflection time
    4:15 pm - 5:15 pm Day 2 Open discussion
    Thursday, January 31, 2019
    8:15 am - 8:45 am Day 3 Continental Breakfast (outside SFI Noyce Conference Room)
    8:45 am - 9:45 am Cooperation and specialization in dynamic fluids - Dervis Can Vural (Univ. Notre Dame) Download Presentation
    9:45 am - 10:00 am Day 3 Reflection time
    10:00 am - 10:15 am Day 3 AM Break
    10:15 am - 10:45 am Collaborative Platform Work Time: references, reference note, presentation upload, additional reflection & commenting on each other’s reflection
    10:45 am - 12:00 pm Day 3 Open discussion
    12:00 pm - 1:00 pm Day 3 Lunch (outside SFI Noyce Conference Room); Adjourn

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    Meeting Synopsis

    An ink drop placed in water will dissolve and homogenize, never to return back to its original state. Many-body processes involving stochastic forces universally and irreversibly lead to entropy maximizing distributions. This working group aims to ask what the analog of ‘dissolving ink’ is in the context of ecological evolution. Specifically, this WG will explore irreversible changes in the ecological interaction structure and their consequences. Of particular interest are theoretical frameworks that incorporate dynamics as well as experimental approaches that can track irreversible transitions in strongly interacting populations. Key foci for this WG are the directionality of the coevolution of interspecific interactions and ecological transitions, and the synthetic control of such transitions.

    Additional Meeting Information
    Abstracts by Presenters

    Samraat Pawar (Imperial College London) - Are changes in species interactions and their ecosystem consequences irreversible?[edit source]

    All interactions between individuals of the same or different species (populations) are metabolically-constrained. That is, the rate of an individual's energy use (metabolic rate) sets the rate of interactions with other individuals. In this talk, I will first describe the relationship between metabolic and species interaction rates as a function of the physical environment as well as the organism's mass, using ecological metabolic theory. I will then describe the effects of (metabolically-constrained) species interactions on the dynamics of ecosystems. Finally, I will consider whether changes in metabolically-constrained species interactions are irreversible.    

    Dervis Can Vural (Univ. Notre Dame) - Cooperation and specialization in dynamic fluids[edit source]

    Community ecology is built on the notion of interspecies interactions. The strengths of interactions are almost invariably taken as fixed parameters, which must either be measured or assumed. The few available models that do consider the formation and evolution of interactions, including some built by myself, are based on ad hoc definitions of fitness. In this talk I will present a first-principles approach to how interactions between and within species change. In this picture, the black box of "interspecies interactions" will be replaced with advection, diffusion, dispersal, chemical secretions and domain geometry. I will show that the fundamental laws of fluid dynamics and the physical parameters describing the fluid habitat determine whether species will be driven towards individualism, social cooperation, specialization, or extinction. I will end my talk by proposing ways to tailoring the interaction structure of a microbial community by manipulating flow patterns and domain geometry.    

    Otto Cordero (MIT) - Cooperative growth and cell-cell aggregation in marine bacteria[edit source]

    Bacterial cooperation, whereby cells secrete compounds that can facilitate the growth of neighboring cells, has been extensively studied through the lens of evolutionary biology. However, the environmental implications of cooperation and the ecological scenarios under which it takes place remain much less understood. In this talk I will discuss the conditions under which cooperative growth emerges in microbial populations that degrade complex organic materials in the ocean. I will show that organisms that are poor secretors of hydrolytic enzymes use chemotactic behavior to form cell-cell aggregates that enable individuals to increase local concentrations and efficiently uptake the solubilized organic matter. By contrast, when organisms secrete highly active enzymes dynamics turn competitive, cells avoid aggregation and the efficiency of carbon uptake drops. I will also discuss the theoretical limits of aggregation and how bacterial isolates from the ocean overcome these limits in the laboratory by developing multicellular behaviors. I will back up these results with theory, data from individual based models and experiments with natural isolates. Finally, I will discuss the potential role of social cheaters in the natural environment, based on a study with hundreds of micro-scale particle colonization experiments in natural seawater.

    Annette Ostling (Univ. Michigan) - Emergent structure and dynamics in stochastic, open, competitive communities[edit source]

    Here I describe recent theoretical work by my lab looking at the emergent patterning in models where niche differentiation acts in concert with drift and immigration, as well as empirical work looking for that patterning. The results of our study of “stochastic niche communities” provides further generalization of the recent theoretical developments suggesting that niche differentiation may actually lead to clusters of species similar in traits, in contrast with traditional expectations of even spacing or overdispersion. These traditional expectations are derived from models ignoring stochasticity and immigration as well as other factors. I will review both classical and more recent theoretical developments along the way. We also find niche differentiation plays a more complex role in species persistence in stochastic niche communities than classically expected, enhancing persistence of a select few species, and lessening the persistence of others. We have also demonstrated the occurrence of this pattern of clusters across an array of niche mechanisms, and groundtruthed metrics for its detection in field data. Finally, we have applied our metrics to trait and abundance data for tree species in the 50 ha plot on Barro Colorado Island, and find significant clusters in four traits linked to niche axes. I will discuss all of these developments and also highlight connections to the question of irreversibility in the ecological and evolutionary dynamics of competing species.

    Jacopo Grilli (ICTP) - Higher-order interactions, stability across timescales, and macroecological patterns[edit source]

    The difficulty of reconciling the staggering biodiversity found in tropical rainforests with classical theories of resource partitioning has led ecologists to explore neutral theories of coexistence, in which all species are assumed to have the same physiological parameters, and variations in species abundance arise from stochastic fluctuations. Here we propose a theory of coexistence in which all species have different physiological rates, and interact with each other through a network of competitive interactions. We show that our models produce robust coexistence of many species even when parameters are drawn at random. Importantly, the dynamical stability of our models is due to higher-order interactions — interactions involving more than two species at a time. Moving from deterministic to stochastic models, we find that the presence of higher-order interactions, which make equilibrium points attractive, dramatically increases the time to extinction in isolated systems, allowing for the prolonged coexistence of species. When we let the system evolve, we recover many empirically observed macroecological patterns.

    Fernanda Valdovinos (Univ. Michigan) - Irreversible processes in ecological networks[edit source]

    Inspired by the exciting topic of this workshop, my talk will present research by my group that have found irreversible processes in the ecological and evolutionary dynamics of species-interaction networks. The first work I will present evaluates the interplay between the structure and dynamics of plant-pollinator networks when population and behavioral dynamics are incorporated in more mechanistic models of those networks. I will focus on the irreversible dynamics caused by adaptive foraging that may explain why we only observe moderately connected plant-pollinator networks in nature even when pollinator would benefit from fully connected networks. The second work I will present predicts the invasion success of pollinators in plant-pollinator networks and their subsequent impacts on natives. I will focus on the impacts that can and cannot be reversed by restoration practices seeking to remove the invasive species. The third work I will present evaluates the interplay between economic and ecological dynamics governing fishing effort in harvested food webs. I will focus on the irreversible transients that cause a fisheries industry to either thrive or collapse, the harvested species to either go extinct or persist, and food webs to suffer either dramatic cascade extinctions or sustainable harvest. Finally, I will present our work on the evolution of food webs integrating population, speciation and invasion dynamics over evolutionary timescale. I will focus on the irreversible extinctions patterns and whether the specialization tendency found can be reversed by increasing the frequency of perturbations. In my presentation of each of those four projects I will share with you what I still do not understand to hopefully ignite insightful discussion on the specific subjects.

    Greg Dwyer (Univ. Chicago) - Natural selection, population cycles, and climate change in forest insects[edit source]

    Cyclic outbreaks of forest insects devastate forests, leading to widespread defoliation and tree death. Outbreaks would be far worse if not for epidemics of fatal virus diseases, which decimate outbreaking insect populations. The selection pressure imposed by these diseases suggests that natural selection may affect outbreaks, but understanding such effects is impossible with data alone. My lab has therefore used a combination of field experiments and models to test for effects of selection on outbreaks. Our work shows that both heritable host resistance and variation in viral virulence strongly affect outbreaks of the the gypsy moth, Lymantria dispar, an introduced pest of eastern hardwood forests in North America. Over the last few decades, however, an introduced fungal pathogen has competitively displaced the virus. The fungus provides better control, but its survival is much higher when the weather is cool and wet, whereas climate change is likely to cause weather conditions in the range of the gypsy moth to become increasingly hot and dry. By again combining models and data, we have shown that climate change will have a strong negative effect on the gypsy moth fungus, which may lead to the devastation of hardwood forests in North America. A key question is therefore, can the virus make a comeback? Our answers to this question are as yet incomplete, but provide initial chapters in an interesting story about the ecological effects of climate change.    

    Pamela Martinez (Harvard) - Pathogen diversity and negative frequency-dependent selection: consequences for intervention[edit source]

    Understanding how populations respond to selective pressures is an active area of research, of particular relevance for pathogens, which often adapt after the implementation of epidemic control strategies. Yet attempts to anticipate how and when these populations will evolve, are challenging. By looking at population diversity of rotavirus and Streptococcus pneumoniae, we have explored the impact of negative-frequency dependent selection, which tends to confer an advantage to the rare and a disadvantage to the common, in the response to intervention. Our results emphasize the resilience to control measures, and thus low vaccine effectiveness, in pathogens for which frequency-dependent selection is a key driving force.

    Priyanga Amarasekare (UCLA) - Phenotypic evolution in the Anthropocene[edit source]

    Phenotypic traits constitute the interface between the organism and the environment. Adaptive evolution occurs when trait responses to the  environment maximize fitness subject to constraints. These constraints can be morphological, biochemical or genetic.  On the one hand, evidence of rapid evolution in response to environmental perturbations (e.g., pollution, habitat degradation, climate warming) suggests that evolution in response to these novel selection pressures can proceed unconstrained. On the other hand, evidence of extinctions and disruptions of species interactions suggests that constraints can impede evolution in response to novel selective regimes.  There is much we do not understand about the interplay between selection and constraints, particularly in light of anthropogenically-induced selection regimes.  I am particularly interested in the role of biochemical constraints in reaction norm evolution.  This interest is fueled by my work on temperature effects on ectotherm life history, population dynamics and species interactions.  I want to gain a mechanistic understanding of biochemical constraints all the way from protein folding to enzyme kinetics so that I can incorporate these mechanisms into models of reaction norm evolution.  There is a great deal I do not understand about these processes themselves and how they translate into the mathematics of population dynamics.  I do, however, entertain some speculations about the role of how biochemical constraints in irreversible outcomes in phenotypic evolution.    

    Stephen Proulx (UCSB) - Population genetics of low-probability transitions[edit source]

    I will discuss several examples from population genetics and adaptive dynamics where the probability for a transition between “equilibrium” states is very low. These situations can occur when stochastic environmental conditions create scenarios with alternate stable states that can only be invaded by mutations of large effect, for instance in scenarios with overlapping generations and lottery competition. In a similar vein, when mutations of small effect cause intermediate phenotypes with low fitness, transitions can be rare. Another type of transition involves feedback between the environment and the distribution of population phenotypes, for example in terms of the evolution of mating preferences in combination with the evolution of ecological specialization. Yet another scenario occurs when multiple independent mutations are required to cross an “adaptive valley”. This has parallels in ecological theory, for example with the invasion of novel habitats (e.g. zoonotic diseases). I will encourage discussion of how these different concepts and modes of analysis may be extended to situations with eco-evo feedbacks.

    Robert Marsland (Boston Univ.) - Statistical mechanics of microbiomes[edit source]

    In a seminal paper in 1972, Robert May studied complex ecosystems using Random Matrix Theory. Nearly fifty years later, the rise of quantitative microbial ecology makes it possible to test and refine this approach. Random matrix models successfully capture a wide range of large-scale patterns observed in real microbial communities, including functional and family-level reproducibility, compositional clustering by environment, enterotypes, dissimilarity-overlap correlations, decreased diversity in harsh environments, compositional nestedness, succession dynamics and modularity. After describing the computational model we have developed to reproduce all these patterns, I will present a set of analytic results that explain why this works in the real world. Adding even a small amount of noise to a sufficiently diverse community induces a phase transition to a “typical” phase, where community-level properties such as diversity and rank-abundance curves are indistinguishable from those of a completely random ecosystem. I will explain how the properties of this phase are governed by “susceptibilities” describing the linear response of the ecosystem to small changes in population sizes or resource concentrations. These susceptibilities can be obtained from Random Matrix Theory, in the spirit of May’s paper, and can also be measured by subjecting a community to controlled perturbations.

    Post-meeting Summary by Organizer[edit source]

    Coming soon

    Additional Post-meeting Summary by Organizer

    Post-meeting Reflection by Presenter

    Jacopo Grilli (ICTP) - Higher-order interactions, stability across timescales, and macroecological patterns Link to the source page[edit source]

    Pamela Martinez

    Connection between population dynamics and strain diversity. What is the response to pathogen intervention? (clear in a Chessonian framework, unclear when there is strong strain diversity). 1) Rotavirus. Robust antigenic diversity. Estimate of the parameters from cases: G-type strong specific immune response, P-type strong general immune response (concern: very few data, enough statistical power). Surprising: no effect of vaccine/intervention. 2) S. pneumonia. Frequency of strains. How does frequency change after intervention? Replicator model, predicted fitness from genes (how? Not clear): can predict frequencies after intervation (which again does not work). Questions: 1) what determines the equilibrium frequencies of genes? Why loci are under negative frequency negative dependent selection?

    Annette Ostling

    Stochastic open competitive communities. Niche/unique opportunities/deterministic forces vs chance/neutral/stochastic forces. Finding niche differences is a challenge. Stochastic Lotka-Volterra on 1dim niche axis . Cluster emerge. 1) Metric. What is a good measure of clustering and how is that affected by different mechanisms? 2) Data. BCI and regional pool.

    Greg Dwyer

    Gipsy moth & virus/fungi. Inference of parameters from time-series. Key ingredient: variability of susceptibility between individuals. Works in reproducing data (but it is hard to predict)

    Otto Cordero

    Hyper-diversity of microbial communities. How do we interpret that diversity? Patches of organic matters (~detritus) are hotspots of diversity: multiple species are recruited. Lab experiment: biopolymers, 100 species. -Omics + culturing + phenotyping in order to recostruct dynamics. Observed successions (are true successions? Can also be explained by variability in growth/dilution rate). How succession depends on niche-breadth? Idea: niche breadth is bimodal (small niche breadth: early colonizers, specialized. Large niche breadth: late colonizers, cannot be grown in culture). He then looks at the metabolic networks: close to the central metabolism everything is more homogeneous, close to the periphery everything is more heterogenous (high variability in copy number). He then plots #of chitinases vs the # of coevolved modules. Early colonizers are high in both. Late colonizers are low in both. Free loaders have high # of coevolved modules but low #chitinases (can eat what free riders eat). Ecological dyanmics is consistent with this classification (degraders grow initially and then decay, cheaters and cross-feeders grow later)

    Robert Marsland

    Two facts: A) Microbiome is very diverse. B) Taxa is unstable, function is stable (robust patterns). Assumptions: 1) classical ecological models are inadequate for understanding ecosystems 2) large / diverse ecosystems are typically random. (Random) Chemostat model predicts many patterns. Why random works well? Above stability threshold random works very well.

    Priyanga Amarasekare

    1) Phenotypic traits are the interface between organisms and the environment 2) Evolution: (mutation+)contraints+selection 3) Irreversible processes arise from contraints. Different types of contraints: genetic (evolution acts only on heritable traits), energetic (tradeoffs), morphological (upper limits to evolutionary trajectories). Rest of the talk on how different traits depend on environment (Temperature). Two mechanism for reaction (to T variaton) norm: enzyme activation (monotonic response, e.g. mortality) and regulatory/hormonal (unimodal shape, e.g. eggs maturation) -> conserved across taxa.

    Fernanda Valdovinos

    Samraat Pawar

    Stephen Proulx

    Dervis Can Vural

    OPEN DISCUSSION. 3 themes/questions


    1) Identify quantities that are always increading or decreasing.

    (side questions: why? At what scale (temporal, spatial, ...) do they have that trend?

    Possible examples (in a Markov chain): return time (as a measure of irreversibility), turnover time, how often the system returns to the original state, fraction of trajectories that go from A->B vs from B->A.

    Possible examples (interpretable quantities): # of species, biomass, # of limiting resources, # of niches, properties of resource consumption (e.g. efficiency), degree of specialization, interdependence, major (evolutionary) transitions

    Question1- quantities to measure.jpg

    2) List of properties that we expect to be reversible/irreversible

    Irreversible: oxygenation event (major transition), increase of specialization, latitudinal gradients, adaptive radiation, cluster formation

    Debated: drift, mass exctintion (in what sense they are irreversible)

    Reversible: function(?), total biomass (?)


    3) (relevance of) transients

    It depends on the timescale of evolution vs population dynamics.

    Relevance of timescales: timescale of evolution, environmental change, behavior vs timescale of population/community dynamics

    Relevant examples: patterns of extintions (position in transient determines outcomes), cycles ("always" in a transient)

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    Dervis Can Vural (Univ. Notre Dame) - Cooperation and specialization in dynamic fluids Link to the source page[edit source]

    To discuss: Could we make a grocery list of all irreversible processes mentioned in the workshop? Few that come to mind immediately: (1) Priyanga's idea on hot to cold invasion (2) Ecological succession. (3) Niche filling (4) something funky happens with the lottery model when there is a big mutation event (is there a name for this? Surely it is a generic thing that can happen in many other systems) (4) formation of interdependences / mutualism / specialization (I will mention in my talk tomorrow) (5) gene duplication (I couldn't follow all there steps here). Anything else I'm missing?

    More specific thoughts on individual talks:

    Otto Cordero:

    Succession of species on hydrogel microspheres. Otto uses spheres with four kinds of nutrition. (1) why are species either specialist (able to digest only one type of sphere) or generalist (able to digest all types). (2) Why don't the cheaters (those who do not produce digestive enzymes) take over. (3) Prima facie, I would expect cheaters to have much lower detachment rate. They should just stick onto spheres and wait for the digestive bacteria to arrive. For the bacteria doing the work a better strategy is to detach quicker, at least before cheaters arrive. Is this observed in experiments? (4) is the interaction between bacteria indirect (i.e. they compete for the same resource) or do they secrete antibiotics or consume one other? (5) what is the role of diffusion lengths? The commensalist bacteria (those who do not secrete enzymes, do not compete for the main resource, but utilize the metabolic byproducts of others) gather whatever they can within diffusion length. So we can calculate the limit the number of layers of bacteria on a surface. For resources (e.g. dead crab shells) that are smaller than the diffusion length, the shape and size of the resource will also make a difference. Also calculable.

    Pamela Martinez:

    Markov process to describe the spread of pathogen with multiple serotypes (a kind of SIR model). How to differentiate between different models with sparse data. Data could be equally consistent with randomly connected states or even a single Poisson process with appropriate mean. A good suggestion during the talk: generate synthetic sparse data using the model, pretend the data is real, and estimate model parameters. Do they have a similar value? (1) why does the efficacy of vaccines not show up in the population data (they do make a significant difference in controlled studies). (2) why does the vaccine work on some countries but not the others (3) Rotavirus somehow interacts with the gut microbiome. There is some literature that shows that vaccines work for people with microbiomes of the "european kind".

    Annette Ostling

    Starts with Lotka-Volterra type fitness function. Species are assigned traits between 0-1 and and the interaction matrix is structured such that species with similar traits antagonize each other. This is done with a gaussian kernel in the sum. Questions: (1) what determines the number of clusters. Can I use Turing analysis to solve this analytically? (2) Can I view phylogenetic branches as "clusters"? e.g. animal kingdom, plant kingdom etc. are, in some sense, clusters. And then, there are sub-clusters within these clusters, and sub-sub clusters. What feature should be added to the model to obtain sub-clusters. (3) Given an empirical distribution of features (within a species or within multiple species supposedly filling a niche) how do I distinguish between environmental filtering vs exclusion?

    Priyanga Amarasekare: Her argument is, species respond to temperature in an "asymmetric way" (specifically, you hit a wall at high temperatures, but the negative response to cold is more gradual). This leads to an irreversible flow of species (via mutant invasions) from hot regions to cold ones. Comments: (1) I like the idea a lot, very plausible. Here is my alternative (and quite possibly false) point of view: A high population is more evolvable, because there will be more mutants/innovation. Warmer climates have higher biomass (just because it receives more energy) and will therefore generate viable invaders at a higher rate. Maybe.

    (2) She had some discussion about constraints vs selection. It's a possible to dichotomize, but I view these two things as one thing. A constrained region in phenotype space is just one with fitness=minusinfinity, so no one visits there. Possibly just a matter of semantics, but in any case, I don't see how a constraint implies irreversibility.

    Jacopo Grilli: Three-body interactions surprisingly stabilize the community (unlike those with two-body interactions). I found this surprising because the model with three-body interactions is really an effective model of a two-body interactions. e.g. species A,B,C come together; first A interacts with B, then the winner interacts with C. (and you symmetrize this, because sometimes first A interacts with C first). As such, the outcomes of this model should reduce to a Lotka-Volterra model, (with specific structure, under specific conditions). However, I was not able to figure out what this structure is, and what the conditions are. Whatever the structure and conditions, the stability of the system with three-body interactions should not be a surprise if the equivalent Lotka-Volterra equations are also stable. Either way, I would like to understand this better.

    Greg Dwyer: The viruses that infect the pests have multiple DNA's, so I thought that might give rise to an interesting cooperation/cheating dilemma, similar to the one we see in sperm trains. Also there is an interesting three-species coevolution going on between the pests, and the virus and fungus that infect the pests.

    Greg likes things he can measure and doesn't like discussing the meaning of life. But then he was converted, and found the meaning of life. Turns out meaning of life is measurable after all.

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    Annette Ostling (Univ. Michigan) - Emergent structure and dynamics in stochastic, open, competitive communities Link to the source page[edit source]

    Darwin's arrow of time versus the 2nd law

    Life on earth is subject to constant energy input from the sun. The 2nd law of thermodynamics, that entropy should increase, is for a closed system. So it seems it is not even really relevant for thinking about life on earth.

    Definitions of irreversibility

    One key definition of irreversibility we discussed is that if you reversed time the process would look strange—abiological. Can we make that definition more quantitative? Perhaps we mean simply that it would be going against changes predicted by the selective regime or expected population dynamics? Can we make that definition accommodate degrees of irreversibility, e.g. looking backwards involves changes less likely to happen? This fits in with what Priyanga talked about with adaptation to colder being easier than adaptation to warmer due to the shape of the relationship between the performance and temperature.

    BUT is this definition too broad? Any system with an equilibrium point is irreversible in this sense, because if you reversed a time series of it approaching its equilibrium it would not make physical/biological sense?

    So do we really need to add something more to that definition, perhaps to include the idea that some environmental variable is being changed in time and we are watching the response to it, and asking if the system would go back if we changed the environment back? In that case our definition of irreversibility is the presence of hysteresis?

    Is another definition of irreversibility that the system changes in a way that impacts its future potential changes or response to change in the environment? Or maybe this is just something often associated with irreversibility, as it is not the same as asking about a reversal of time, but instead whether there is path dependency in the system? Is this question of path dependency related to Gould’s question about whether replaying the tape of life would lead to the same outcome?

    An example of this idea of the change in the system impacting potential response to future change is the case of competitive cluster formation (see below). If one assembles the community under one environmental filter, and then the environmental filter changes, community biomass may go down and never achieve what it was before or could have been under new environmental regime if assembled that way in the first place. The idea is that the change in environmental filter may not have be strong enough to overcome competitive footholds species have in the community. 

    Drift and selection, and is drift reversible?

    Two key processes in ecology and evolution are drift and selection (among species or among alleles). Is drift in a sense a force creating more disorder? If so, we would think it would increase entropy in a sense and lead to irreversible changes? (Note there has been one paper by Sella and Hirsh in 2005 in PNAS trying to think about drift as something increasing entropy and more broadly a "free fitness" function like a "free energy" function, summarizing the role of selection and drift in the state of the population.) But we discussed it yesterday as reversible. Can we be more quantitative about why we think about it as reversible?

    Further, is drift really reversible? Drift can prevent a system from reaching another fitness peak, by causing loss of advantageous, neutral, or disadvantageous alleles when they are rare. (Recall the stochastic tunnelling examples Stephen Proulx talked about for how evolution may overcome this however.) So it can change the future possibilities for the system. It can also be involved in the somewhat irreversible process of competitive cluster formation (see below). A particular species may gain high abundance by chance (drift) and then have a stronger influence on the the competitive landscape for other species and become abundant in its cluster. Actually if there are no edges and no environmental filter, drift one of the two key ingredients in cluster formation (the other being initial conditions).

    Key idea related to irreversibility and questions I raised in my talk

    In my talk I highlighted that the formation of species clusters on trait axes under competition has some degree of irreversibility, in the sense that under strong competitive sorting, once a species dominates a particular cluster it is unlikely to loose its foothold. It would take a strong perturbation in species' abundances, or a change in which species are favored by the environment, to change which species would dominate in each cluster. Further, once certain species have gained a foothold in each cluster, this influence any subsequent assembly or evolution (selection, speciation, extinction) in the community.

    The questions I posed about this particular phenomenon of irreversibility are:

    1) How is the rate of competitive sorting, i.e. the strength of cluster formation, and hence degree of irreversibility, shaped by the mechanisms of competition? Do clusters emerge for all realistic competition mechanisms?

    2) How will cluster formation depend on spatial scale, and how will this be influenced by the strength and scale of dispersal, relative to the scale of any heterogeneity involved in niche differentiation mechanisms?

    3) Is the irreversibility of community pattern formation a particular concern for communities that may become isolated? These communities will experience extinction debt, and afterwards their resilience to environmental change may be low (the species that may be favored by the new environment may be gone).

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    Fernanda Valdovinos (Univ. Michigan) - Irreversible processes in ecological networks Link to the source page[edit source]

    Pamela Martinez:

    Very interesting research on how strain diversity can affect disease spread. I learned a lot about best practices on how feetting models to data because of the discussion this work provoked.

    Annette Ostling:

    Impressive work of testing the prediction of a competitive model of plant species with empirical data. The authors found that clustering happens in tropical forests due to niche partitioning. I learned much on different competitive models.

    Greg Dwyer:

    This talk was very useful for me to understand ways in which empirical data and models can interplay to make concrete predictions that can inform management. The applied case of informing agencies when to spray the forest with virus to stop the tree disease was very illuminating.

    Otto Cordero:

    Interesting application of ecological theory to microbial communities. I really enjoyed the way the speaker identified biological mechanisms in his empirical system and was able to connect the modeled dynamics to those empirically tested mechanisms.

    Priyanga Amarasekare:

    This talk made me think in a deeper way about constraints on phenotipic/genotipic variation that can help us understand how ecological system may respond to human perturbations such as climate change.

    Fernanda Valdovinos (my talk):

    It was extremely helpful for my research the in depth discussion that the audience provoked on the details of my model. The dissecting questions I received on my equations and their consequences were very illuminating. I will definitely use some of the new understanding I acquired trough answering those questions in the paper I'm currently working on. I also really appreciate the philosophical question that Greg asked me over the break and Jacopo helped to answer. That question was about what are we actually learning by using a network approach instead of just many differential equations as we have been doing for years in ecology prior networks. I would really like to further discuss this question as a group tomorrow.

    Stephen Proulx:

    Amazing talk that helped me better understand adaptive dynamics, how we can read mutation/invasion maps and how to make better use/understanding of fitness landscapes. It was fascinating to me the trade-off example on plant fertility-survival that showed a clear case in which small vs large mutations can drive the genotype/phenotype of plants to different attractors. I also liked a lot one of the speakers questions on how to produce general theory from non-equilibrium cases and the discussion that question provoked.

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    Greg Dwyer (Univ. Chicago) - Natural selection, population cycles, and climate change in forest insects Link to the source page[edit source]

    Pamela's presentation reminded me of the importance of basic competition theory in understanding competition between pathogen strains, specifically in terms of the interplay between frequency-dependent and density-dependent selection in the insect pathogens that I study. That has in turn helped me to begin to see how theory of pathogen competition is related to more general theories of competition, as Priyanga pointed out, and as became clear from seeing Annette's and Otto's and Bobby's presentations.

    Something I am unclear on, however, is how and whether such theory of such generality has practical implications for pest control. Those comments apply even more strongly to the whole idea of irreversibility. I can see what Dervis and Jacopo mean by "ecological irreversibility", but I can't see the practical applications. Meanwhile, I can't see what David Krakauer's ideas have to do with killing pests in any way. That said, I can appreciate that I may need to think about all these ideas quite a bit more.

    My first 2 paragraphs were based on the first day of talks. Now that the meeting is done, I have 2 more thoughts. Off and on during the meeting, we had long rambling discussions about the semantics of irreversibility. I found much of that discussion to be a waste of time. After the meeting was over, however, we were able to identify metrics of irreversibility, and those metrics will be directly useful in work in my lab.

    Questions I would like to know the answer to, and that are motivated by the talks I've listened to:

    Is the outcome of pathogen competition irreversible, or can it be reversed by climate change?

    To what extent are high-level abstractions useful in understanding ecological problems, and in applied ecology more specifically?

    Are statistically robust tests of ecological theory necessary for the theory to be useful?

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    Priyanga Amarasekare (UCLA) - Phenotypic evolution in the Anthropocene Link to the source page[edit source]

    1. Presentation highlights: (i) The role of constraints in phenotypic evolution as means of generating irreversible evolutionary endpoints and set upper limits to evolutionary trajectories. (ii) Role of constraints in species' ability to adapt to changing environments. (iii) Species come up against hard limits to phenotypic plasticity under climate warming. (iv) In order for thermal reaction norms to evolve in the face of climate warming, there has to be genetic variation. Unclear that reaction norms under strong biochemical control (e.g., development) have sufficient amounts of variation for the upper thermal limit to evolve in response to warming.

    2. Open questions:

    2.1 Connection between Darwinian adaptationist evolution and the idea of increase in disorder (as in the second law of thermodynamics)

    2.2 What exactly are irreversible evolutionary endpoints? Can we come up with a specific definition of irreversibility?

    2.3 Selection and constraints are not the same thing. This needs to be clarified.

    3. How my perspective has changed: I want to think more carefully and deeply about the connection between Darwinian evolution and the second law of thermodynamics.

    4. Reflections on other presentations

    4.1 Stephen Proulx - I very much liked this presentation about the population genetics of low-probability transitions. I was particularly interested in stochastic selection due to lottery competition that leads to alternative stable states making it possible for mutations of large effect to cause transitions between states in a directional manner. I also liked the models of stochastic tunneling or valley crossing, that provide possible avenues for transitions between states. The case of multiple independent mutations enabling valley crossing is equally fascinating. I particularly liked how the examples shown related to the central theme of irreversibility and transitions.

    4.2 Dervis Can Vural - An elegant presentation of the evolution of cooperation against the backdrop of fluid dynamics. I would like the theory to be generalized to perturbations other than shear so that it can also apply to pathogenic microbes within a host and other situations that do not involve fluid as a medium. I think you also should take the plunge and try to connect this theory to Hamilton's theory of kin selection. It is hard, and perhaps not analytically tractable, but it would be worth doing.

    4.3. Samraat Pawar - I like the connection between metabolic constraints on species interactions and carbon fluxes.

    4.4 Fernanda Valdovinos - The idea that adaptive foraging by mutualists (e.g., pollinators) allowing the persistence of nested mutualistic networks is a novel and exciting finding that pushes the field forward.

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    Robert Marsland (Boston Univ.) - Statistical mechanics of microbiomes Link to the source page[edit source]

    Questions from my talk:

    True or false?

    1. Classical ecological models are inadequate for understanding microbial ecosystems.

    2. The large-scale, reproducible patterns we see across microbiomes are emergent features of “typical random ecosystems.”

    3. Diverse communities will almost always behave like “random ecosystems.” 

    Question I want to discuss

    Can large-scale ecological changes over time be understood through simple general principles? (Samraat, Jacopo, Priyanga, me: flux balance/metabolic rates, random matrix theory, biochemical and morphological constraints)

    Are there ecological summary statistics that change monotonically over time? (Jacopo, and some of my work that I didn't talk about -- see references)

    Which properties of individual organisms are essential for predicting large-scale ecological changes?

    - Pamela -- why do some vaccines fail to produce large-scale ecological change (i.e., pathogen extinction)?

    - Greg -- importance of distribution of susceptibilities to dynamics of epizootic onset.

    - Fernanda -- importance of adaptive foraging for understanding why pollinator systems don't collapse -- and why they might under new circumstances.

    - Samraat -- taking the mechanics of inter-species interaction seriously, understanding how they affect response of ecosystem to temperature changes.

    - Priyanga -- asymmetry of reaction norms for temperature variation.

    What do we miss when we focus too much on equilibrium/steady states? (Prevalence of cyclic disturbance/recovery dynamics -- Greg, Samraat)

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    Samraat Pawar (Imperial College London) - Are changes in species interactions and their ecosystem consequences irreversible? Link to the source page[edit source]

    It was encouraging to see that people were intrigued by and interested in the issue of non-equilibrium/steady-state dynamics. Dervis asked a very pertinent question about the appropriateness of the Arrhenius equation for the temperature dependence of population growth rate and other "higher-level" processes.

    Robert Marsland[edit source]

    Fascinating work -- the mathematical model opens up interesting new avenues for theoretical development for microbial ecosystem theory. The statistical mechanical approach, and the discussion about links to Lotka-Volterra type models and random matrix theory (including Robert May's results) were very insightful. The possible links to Otto Cordero's empirical results were exciting to see. Later Bobby and I discussed the possibility of of including temperature and size-scaling effects, and extensions of the model to include phytoplankton as well. These papers are relevant from this perspective:

    • (An analysis of thermal responses of bacterial and archaeal growth rates)
    • DeLong, J. P., Okie, J. G., Moses, M. E., Sibly, R. M. & Brown, J. H. Shifts in metabolic scaling, production, and efficiency across major evolutionary transitions of life. Proc. Natl. Acad. Sci. U. S. A. 107, 12941–12945 (2010). (size scaling of microbial metabolic and growth rates)
    • Tang, S., Pawar, S. & Allesina, S. Correlation between interaction strengths drives stability in large ecological networks. Ecology Letters 17, 1094–1100 (2014). (example of using metabolic constraints to parameterize random matrix theory/model).

    Pamela Martinez[edit source]

    Intriguing results about inconsistency between data and inferences that have been drawn in the past about the efficacy of antibiotics. This paper might be interesting/useful:

    • Cruz-Loya, M. et al. Stressor interaction networks suggest antibiotic resistance co-opted from stress responses to temperature. ISME J. (2018). doi:10.1038/s41396-018-0241-7

    Annette Ostling[edit source]

    The clustering of trait values on nice axes is a cool result. I think constraining the Niche-Neutral assembly model's parameters using ecological metabolic theory (especially, size-scaling) would provide further insights, and could lead to more precise predictions about the clustering of traits. I know Annette has published one on neutral theory constrained by size scaling (O'Dwyer, J. P., Lake, J. K., Ostling, a, Savage, V. M. & Green, J. L. An integrative framework for stochastic, size-structured community assembly. Proc. Natl. Acad. Sci. U. S. A. 106, 6170–5 (2009)). More to do along those lines, especially as competitive interactions too are strongly determined by size scaling and thermal responses. Our recent paper on phytoplankton competition is relevant:

    • Bestion, E., García-Carreras, B., Schaum, C.-E., Pawar, S. & Yvon-Durocher, G. Metabolic traits predict the effects of warming on phytoplankton. Ecol. Lett. 21, 655–664 (2018).

    Greg Dwyer[edit source]

    Fascinating study -- remarkably detailed modelling and model fitting to data! Raised in my mind again the (seemingly eternal) question question that biologists face about models: specific or general? The problem of Fungus vs Virus would benefit by characterizing their temperature-dependence in vitro.

    Otto Cordero[edit source]

    Very interesting study. Particularly useful to me as my lab is increasingly focusing on microbial ecosystem dynamics. The idea of using artificial nutrient particles/spheres is really innovative! The repeatability of bacterial community/network assembly / succession / turnover is striking. The low efficiency (~20%!) of uptake/use of metabolic byproducts was interesting to hear about -- looks like diffusion/turbulence/mixing plays a big role. Makes me wonder about the effect of turbulence/mixing on these dynamics (something we are particularly focused on in our modelling). The fact that early succession bacteria are more motile was also very interesting. Some of the detail about strategies adopted by generalist bacteria was particularly interesting.

    Priyanga Amarasekare[edit source]

    The Hawaiian Tree-creeper example was a great start to open a real debate! I guess the question is about irreversibility of timescales -- given enough time, is a reversal of beak morphology really impossible? I think the evidence for traits such as attack rates, which occur and are measurable at short timescales have a less right-skewed was not quite convincing. I don't quite understand why attack rates should be hormonally regulated - the onset of foraging by a consumer may be hormonally regulated, but once a consumer is foraging, the interaction rate should be under biochemical (enzyme kinetic) control. However, I do agree that the temperature-dependence of certain rates/traits that are the result of an organismal process integrated over a longer timescale, may have a different, potentially less right-skewed response because of hormonal and other type of regulation. Worth doing a detailed analysis, using a wider range of organisms, I think. the new version of BioTraits would be suitable for this. I have invited Priyanga to participate in this year's VectorBiTE meeting ( in Italy which I am co-organizing, where we could discuss this further and perhaps undertake such an analysis.

    Fernanda Valdovinos[edit source]

    Very interesting model with interesting results! I found it strange that plants can produce nectar without cost. Perhaps as Fernanda said, this is a negligible factor, but would have been good to see some evidence for this, and some exploration of the model's structural robustness. But the approach of modeling the rewards as a separate pool with its own dynamics and imposing adaptive foraging altogether provided me with interesting new insights. I think that using movement biomechanics for bounding the interaction/visitation rates of pollinators would be worthwhile.

    Dervis Vural[edit source]

    Very cool work. I absolutely agree that a mechanical approach towards understanding microbial interactions and evolution/co-evolution is the way forward. I raised the point (maybe too many times!) that organismal properties (locomotion) and environmental temperature need to be added to such modelling/theory. Also, why no turbulence? But overall, I found the results really insightful. I agree with Dervis' idea/claim that a general theoretical framework that allows the physical environment's properties to constrain interactions (and their ecological/evolutionary outcomes) within and between populations is possible and necessary. This is also the message I was trying to deliver in my talk.

    Jacopo Grilli[edit source]

    Much-needed formalization of higher-order interactions, with compelling results. Would need some work to reconcile/test with empirical data, but a important step forward, I thought. The issue of indirect (e.g., trophic cascades) vs higher-order interactions (e.g., modification of a pairwise interaction by a third agent) came up. There is considerable confusion in the literature and even among us as to what the two terms entail. Indirect interactions are not the same as higher-order interactions, but ecologists very often use them interchangeably. There is a recent Ecology Letters paper that also tries to get at the distinction between the two:

    Terry, J. C. D., Morris, R. J. & Bonsall, M. B. Trophic interaction modifications: an empirical and theoretical framework. Ecol. Lett. 20, 1219–1230 (2017).

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    Stephen Proulx (UCSB) - Population genetics of low-probability transitions Link to the source page[edit source]

    My two questions:

    1) How can we incorporate analyses of non-equilibrium dynamics *and* be able to make general theory?

    2) How often do ecological feedbacks results in bi-stable evolutionary states?

    Following up on my first question about non-equilibrium dynamics: We had a discussion of how to analyzed and communicate these kinds of results in publications. It seems that there is a missing set of tools to be able to categorize and communicate these kinds of results.

    Pamela Martinez:

    One of the ideas here was that frequency dependent selection could lead to coexistence, but also that this coexistence was complicated by environmental variability. The model fitting approach involved modeling both process and observation error, and some of the results were consistent with relatively constant total levels of infection even while reported cases could still vary.

    Robert Marsland:

    Some of what I was particularly interested in from this talk was liking the May type stability analysis to some sets of more mechanistic models. It was really interested in the possibility that the transition between communities that allowed as many species as niche to coexist and as the noise level goes up then the system transitions to maintaining only half the species.

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    Post-meeting Reflection by Non-presenting Attendees

    Susan Fitzpatrick (JSMF) Link to the source page[edit source]

    The work on vaccines presented by Pamela clearly makes a connection across working groups. As the role of immune function and aging become increasingly of interest be interesting to think of how the effectiveness of vaccines changes across life spans - including of the vaccine and those vaccinated.

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    Nathaniel Rupprecht (Univ. Notre Dame) Link to the source page[edit source]

    Annette Ostling:

    Suppose that more similar species compete more directly - a very reasonable assumption given the reality of the fuzziness of defining species. Then an LV equation can have species parameterized by "traits." Different "niches" arise naturally in this model. A study of traits in a Panamanian forest suggests that species cluster in trait niches. Question: the niche peaks tend to "repel" each other - is it worthwhile to think of individual peaks as species "quasiparticles" that interact with nearby quasiparticles through some generalized interaction, thereby giving rise to large scale, slow time dynamics?

    Otto Cordero:

    By creating nutrient beads and immersing them in seawater, colonization by bacteria can be studied in a controlled way. Genomic signatures can be mapped to particular strategies - degraders, cross-feeders, and cheaters. Question: Does the geometry of the beads have an effect on the time behavior of populations? In other words, if instead of spheres, the bacteria were left to colonize tori or sheets, would there be any noticeable differences?

    Priyanga Amaraserkare

    Interested in when species are able to adapt to new environments. One take away is that species die much more quickly when introduced to high temperatures as compared to low temperatures, and that rate controlled processes have a different functional dependence than regulatory (as a function of temperature). Another very interesting point: it is very common for species from the tropics to invade more temperate climates, but it is much more unlikely for a temperate species from higher altitudes to invade a tropical environment.

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    Sushrut Ghonge (Univ. Notre Dame) Link to the source page[edit source]

    A. A group of few simple species can evolve into a large number number of interdependent species. There is an information theoretic entropy increase in this process. This means that if you reach into the ecosystem and randomly pick a species, you are more uncertain about what you will find that you were initially.

    B. There could also be a more direct irreversibility associated with ecosystems: do larger and more complex organisms like us generate more heat (and hence entropy) than simpler organisms? This will need to be answered experimentally. How does entropy production per unit time compare among 100kg of bacteria, 100 kg of insects and a human weighing 100kg? Are complex organisms more efficient at using energy and resources than simpler organisms?

    C. Jacopo's discussion on evolutionary games reminded me of a paradoxical class of games called Parrondo games. These games involve a combination of games that are all losing games, but when played in succession lead to a winning strategy. They have recently been used to explain some ecological and biological features (see references within the link).

    Pamela: Could you please post references and /or tell us about the data pump techniques you used?

    Fernanda: I like your philosophical idea of finding interactions where all organisms benefit. The second law does work against us by stating that for order to increase somewhere, there must be disorder created elsewhere. However, I do not agree that two species that mutually benefit must compete with or harm a third species. They could be harnessing energy from abiotic sources such as the sun, wind or thermal vents. Is it mathematically possible to have systems with only positive interactions between the living components? Are there any such systems on earth?

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    Reference Materials by Presenting Attendees[edit source]

    Dervis Can Vural (Univ. Notre Dame) - Cooperation and specialization in dynamic fluids[edit source]

    Title Author name Source name Year Citation count From Scopus. Refreshed every 5 days. Page views Related file
    The organization and control of an evolving interdependent population Dervis C. Vural, Alexander Isakov, L. Mahadevan Journal of the Royal Society Interface 2015 5 1
    Shearing in flow environment promotes evolution of social behavior in microbial populations Gurdip Uppal, Dervis Can Vural eLife 2018 5 0
    Increased Network Interdependency Leads to Aging Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2013 0 0

    Annette Ostling (Univ. Michigan) - Emergent structure and dynamics in stochastic, open, competitive communities[edit source]

    Title Author name Source name Year Citation count From Scopus. Refreshed every 5 days. Page views Related file
    The application of statistical physics to evolutionary biology Guy Sella, Aaron E. Hirsh PNAS 2005 0 5

    Fernanda Valdovinos (Univ. Michigan) - Irreversible processes in ecological networks[edit source]

    I uploaded the three papers I presented in my talk:

    Valdovinos et al (2013), Oikos: here I propose the model for the first time and use empirical networks.

    Valdovinos et al (2016), Ecology Letters: Main results I presented in my talk. Niche partitioning via adaptive foraging reverses the effects of nesteness and connectance on species persistance in plant-pollinator networks.

    Valdovinos et al (2018), Nature Communications: I used my model to generate a predictive framework on the invasion of alien pollinators and the subsequent effect on native species within plant-pollinator networks.

    Brosi & Briggs (2013), PNAS: This is the data we used to test the prediction of my model on pollinators preferring specialist plants, when standardizing by plant and pollinator abundances.

    Title Author name Source name Year Citation count From Scopus. Refreshed every 5 days. Page views Related file
    Adaptive foraging allows the maintenance of biodiversity of pollination networks Fernanda S. Valdovinos, Pablo Moisset de Espanés, José D. Flores, Rodrigo Ramos-Jiliberto Oikos 2013 64 6 [ Download]
    Niche partitioning due to adaptive foraging reverses effects of nestedness and connectance on pollination network stability Fernanda S. Valdovinos, Berry J. Brosi, Heather M. Briggs, Pablo Moisset de Espanés, Rodrigo Ramos-Jiliberto, Neo D. Martinez Ecology letters 2016 42 1
    Species traits and network structure predict the success and impacts of pollinator invasions Fernanda S. Valdovinos, Eric L. Berlow, Pablo Moisset De Espanés, Rodrigo Ramos-Jiliberto, Diego P. Vázquez, Neo D. Martinez Nature Communications 2018 22 3
    Single pollinator species losses reduce floral fidelity and plant reproductive function Proceedings of the National Academy of Sciences 2013 0 1

    Greg Dwyer (Univ. Chicago) - Natural selection, population cycles, and climate change in forest insects[edit source]

    Paez et al. (2017) and Fleming-Davies et al. (2015) represent about 2/3's of the results that I presented in my talk.

    Title Author name Source name Year Citation count From Scopus. Refreshed every 5 days. Page views Related file
    Eco-Evolutionary Theory and Insect Outbreaks The American Naturalist 2017 0 0
    Effects of host heterogeneity on pathogen diversity and evolution Ecology Letters 2015 0 2

    Otto Cordero (MIT) - Cooperative growth and cell-cell aggregation in marine bacteria[edit source]

    During Annette Ostling's talk, I mentioned this study, which finds "clusters" in trait space emerging without explicit assumptions about niches. I think Jacopo may find it interesting as well.

    Title Author name Source name Year Citation count From Scopus. Refreshed every 5 days. Page views Related file
    Microbial interactions lead to rapid micro-scale successions on model marine particles Manoshi S. Datta, Elzbieta Sliwerska, Jeff Gore, Martin F. Polz, Otto X. Cordero Nature Communications 2016 130 1
    Multitrait successional forest dynamics enable diverse competitive coexistence Proceedings of the National Academy of Sciences 2017 0 2

    Pamela Martinez (Harvard) - Pathogen diversity and negative frequency-dependent selection: consequences for intervention[edit source]

    Title Author name Source name Year Citation count From Scopus. Refreshed every 5 days. Page views Related file
    Differential and enhanced response to climate forcing in diarrheal disease due to rotavirus across a megacity of the developing world Proceedings of the National Academy of Sciences 2016 0 0
    Prediction of post-vaccine population structure of Streptococcus pneumoniae using accessory gene frequencies bioRxiv 2018 0 1
    Frequency-dependent selection in vaccine-associated pneumococcal population dynamics Nature Ecology and Evolution 2017 0 0

    Priyanga Amarasekare (UCLA) - Phenotypic evolution in the Anthropocene[edit source]

    Title Author name Source name Year Citation count From Scopus. Refreshed every 5 days. Page views Related file
    Temperature dependence of the functional response Göran Englund, Gunnar Öhlund, Catherine L. Hein, Sebastian Diehl Ecology Letters 2011 226 13
    The common patterns of nature S. A. Frank Journal of Evolutionary Biology 2009 117 2
    Temperature dependence of the functional response2 Ecology Letters 2011 0 25 Download

    Robert Marsland (Boston Univ.) - Statistical mechanics of microbiomes[edit source]

    "The Minimum Environmental Perturbation Principle" (Marsland et al. 2019) is some new work I didn't include in my presentation, but which is possibly more relevant to the irreversibility theme. The main result is that a wide class of niche models exhibit monotonic increase in the environmental perturbation under successive invasions/evolution. I would love any feedback from the ecologists about references to add, things that are unclear, etc.

    Marsland and England 2017 and Marsland et al. 2015 contain in-depth explanations of the two kinds of “thermodynamic” irreversibility I wrote up on the board.

    Mehta et al. 2018 begins with a discussion of the "bias/variance tradeoff", which is extremely relevant to the use of models with many parameters to make predictions. It also has a section on dimensional reduction and clustering that might be useful to people working with high-dimensional phenotype data. (Note that the wiki didn't allow me to enter the whole author list, which should also include Marin Bukov, Charles Fisher and David Schwab.)

    Momeni et al. 2017 shows some of the ways in which Lotka-Volterra can fail to capture the population dynamics of a generalized class of consumer-resource models.

    Fisher and Mehta 2014 shows how both niche and neutral regimes can arise in Lotka-Volterra dynamics with immigration, depending on the parameter values.

    "Available Energy Fluxes..." (Marsland et al. 2019) contains a full explanation of our microbial consumer resource model in the appendix. The Python implementation can be found at our group github:

    I have also included the original Human Microbiome Project and Earth Microbiome Project data papers, which contain the large-scale patterns I was showing in the presentation.

    Gutenknust et al. 2007 explains some of the subtleties of Bayesian model fitting in a very accessible way, and strongly influenced the way I think about many-parameter models.

    Goldford et al. 2018 contains some of the patterns I was talking about at the beginning of my talk, which are already captured by a preliminary version of the model.

    Title Author name Source name Year Citation count From Scopus. Refreshed every 5 days. Page views Related file
    Structure, function and diversity of the healthy human microbiome A. Scott Durkin, Allison Griggs, Alyxandria M. Schubert, Amy L. McGuire, Anthony A. Fodor, Antonio Gonzalez, Anup A. Mahurkar, Ashlee M. Earl, Asif T. Chinwalla, Aye M. Wollam, Barbara A. Methé, Beltran Rodriguez-Mueller, Bo Liu, Bonnie P. Youmans, Brandi Herter, Brandi L. Cantarel, Brian J. Haas, Bruce W. Birren, Candace N. Farmer, Carl C. Baker, Carolyn Deal, Carsten Russ, Catherine A. Lozupone, Catherine C. Davis, Catherine Jordan, Catrina C. Fronick, Cecil M. Lewis, Cesar A. Arze, Chad M. Tomlinson, Chad Nusbaum, Chandri Yandava, Chien Chi Lo, Christian J. Buhay, Christie L. Kovar, Christina Giblin, Christopher S. Smillie, Christopher Wellington, Clinton Howarth, Craig Pohl, Cristyn Kells, Curtis Huttenhower, Dan Knights, Dana A. Busam, Daniel D. Sommer, Daniel McDonald, David J. Dooling, Dawn M. Ciulla, Dennis C. Friedrich, Diana G. Tabbaa, Diane E. Hoffmann, Dirk Gevers, Donna M. Muzny, Doyle V. Ward, Elaine R. Mardis, Elena Deych, Elizabeth A. Lobos, Elizabeth Appelbaum, Emily L. Harris, Emma Allen-Vercoe, Eric J. Alm, Erica J. Sodergren, Floyd E. Dewhirst, Gary Armitage, Gary L. Andersen, George M. Weinstock, Georgia Giannoukos, Gina A. Simone, Granger G. Sutton, Gregory A. Buck, Harindra M. Arachchi, Heather H. Creasy, Heidi H. Kong, Holli A. Hamilton, Hongyu Gao, Huaiyang Jiang, I. Min A. Chen, Indresh Singh, Ioanna Pagani, Irene Newsham, J. Fah Sathirapongsasuti, J. Paul Brooks, Jack D. Sobel, Jacques Izard, Jacques Ravel, James A. Katancik, James R. White, James Versalovic, Jamison M. McCorrison, Jane Peterson, Janet K. Jansson, Jason R. Miller, Jason Walker, Jean McEwen, Jeffery A. Schloss, Jeffrey G. Reid, Jennifer R. Wortman, Jeremy D. Zucker, Jeroen Raes, Johannes Goll, John C. Martin, Jonathan Crabtree, Jonathan Friedman, Jonathan H. Badger, Jonathan M. Goldberg, Jose C. Clemente, Joseph F. Petrosino, Joseph L. Campbell, Joshua Orvis, Julia A. Segre, Karen E. Nelson, Karoline Faust, Karthik C. Kota, Katarzyna Wilczek-Boney, Katherine H. Huang, Katherine P. Lemon, Katherine S. Pollard, Kathie A. Mihindukulasuriya, Kelvin Li, Ken Chu, Kevin P. Riehle, Kim C. Worley, Kimberley D. Delehaunty, Kjersti M. Aagaard, Konstantinos Liolios, Konstantinos Mavromatis, Kris A. Wetterstrand, Krishna Palaniappan, Kristine M. Wylie, Kymberlie Hallsworth-Pepin, Lan Zhang, Larry J. Forney, Laurie Zoloth, Lei Chen, Leslie Foster, Liang Ye, Lisa Begg, Lita M. Proctor, Lora Lewis, Lu Wang, Lucia Alvarado, Lucinda L. Fulton, Lynn Schriml, Makedonka Mitreva, Manolito Torralba, Margaret E. Priest, Maria C. Rivera, Maria Y. Giovanni, Mark A. Watson, Martin J. Blaser, Mary A. Cutting, Mathangi Thiagarajan, Matthew C. Ross, Matthew Pearson, Matthew Scholz, Michael E. Holder, Michael Feldgarden, Michael G. Fitzgerald, Michelle G. Giglio, Michelle Oglaughlin, Mihai Pop, Mina Rho, Mircea Podar, Monika Bihan, Narmada Shenoy, Nathalia Garcia, Niall Lennon, Nicholas B. King, Nicola Segata, Nihar U. Sheth, Nikos C. Kyrpides, Noam J. Davidovics, Olukemi O. Abolude, Omry Koren, Owen White, Pamela McInnes, Pamela Sankar, Patricio S. La Rosa, Patrick D. Schloss, Patrick J. Minx, Patrick S.G. Chain, Paul Spicer, Peter J. Mannon, Qiandong Zeng, R. Dwayne Lunsford, Rachel L. Erlich, Ramana Madupu, Ravi K. Sanka, Rebecca M. Truty, Richard A. Gibbs, Richard K. Wilson, Richard R. Sharp, Rob Knight, Robert C. Edgar, Robert S. Fulton, Rosamond Rhodes, Ruth E. Ley, Ruth M. Farrell, Sahar Abubucker, Sandra L. Lee, Sandra W. Clifton, Sarah K. Highlander, Sarah K. Young, Scott Anderson, Scott T. Kelley, Sean Conlan, Sean M. Sykes, Sergey Koren, Shaila Chhibba, Shane R. Canon, Shannon P. Dugan, Sharvari Gujja, Sheila Fisher, Shibu Yooseph, Shital M. Patel, Susan Kinder Haake, Susan M. Huse, Tatiana A. Vishnivetskaya, Teena Mehta, Tessa Madden, Theresa A. Hepburn, Thomas J. Sharpton, Thomas M. Schmidt, Toby Bloom, Todd J. Treangen, Todd Wylie, Todd Z. Desantis, Tsegahiwot Belachew, Tulin Ayvaz, Valentina Di Francesco, Vandita Joshi, Veena Bhonagiri, Victor M. Felix, Victor M. Markowitz, Vincent Magrini, Vivien Bonazzi, Wendy A. Keitel, Wesley Warren, William D. Shannon, Wm Michael Dunne, Xiang Qin, Yan Ding, Yanjiao Zhou, Yiming Zhu, Yu Hui Rogers, Yuanqing Wu, Yue Liu, Yuzhen Ye, Zhengyuan Wang Nature 2012 5,565 6
    A communal catalogue reveals Earth's multiscale microbial diversity Aaron Clauset, Aaron R. Jex, Alexandra H. Campbell, Alexandra M. Linz, Allison Berry, Allison E. Williams, Alyssa Cochran, Amnon Amir, Amy Apprill, Andaine Seguinorlando, Anders Karlsson, Andrew P. Rees, Andrew Whitehead, Anna Forsman, Anni Moore, Anson V. Koehler, Antje Gittel, Antonio González, Antonio M. Martín-Platero, Anupriya Tripathi, Asha Rani, Ashish Bhatnagar, Ashley Shade, Aurora MacRae-Crerar, Baddr Shakhsheer, Bazartseren Boldgiv, Beck Wehrle, Benjamin B. Crary, Benjamin D. Shogan, Benjamin L. Turner, Bharath Prithiviraj, Bonnie Laverock, Brenda B. Casper, Brent Stephens, Byron C. Crump, Caitlin Potter, Carol Robinson, Catherine M. Spirito, Catherine Pfister, Cesar Cardona, Chia L. Tan, Chris Freeman, Christopher Quince, Colin J. Brislawn, Colleen T.E. Kellogg, Congcong Shen, D. Lee Taylor, Daniel A. Cristol, Daniel McDonald, Daniel P. Smith, Daniel Van Der Lelie, Daniela Vargas-Robles, Danielle C. Claar, Danilo Ercolini, Dave Shutler, David A. Lipson, David A. Mills, David Armitage, David Garshelis, David Myrold, Diogo Jurelevicius, Dionysios A. Antonopoulos, Donal M. Boyer, Donald A. Walker, Donglai Gong, Donna Berg-Lyons, Douglas C. Woodhams, Duoying Cui, Elizabeth Pilon-Smits, Elliot S. Friedman, Embriette Hyde, Emily M. Landon, Eric A. Dubinsky, Eric Bottos, Eric R. Johnston, Eske Willerslev, Evguenia Kopylova, Ezequiel M. Marzinelli, F. Joseph Pollock, Fabian Michelangeli, Folker Meyer, Forest Rohwer, Francis Q. Brearley, Frédéric Delsuc, Gabriela M. Sheets, Gail Ackermann, Gary M. King, Gavin Collins, George W. Kling, Giancarlo Galindo, Glida Hidalgo, Graeme W. Nicol, Gregory D. Mayer, Gregory Humphrey, Gunnar Gerdts, Haiyan Chu, Hakdong Shin, Hans Peter Grossart, Hebe M. Dionisi, Helen S. Findlay, Hongxia Zhao, Ina Timling, Iratxe Zarraonaindia, Iris I. Levin, Irma D. Fleming, Isaac Gifford, J. Gregory Caporaso, Jack A. Gilbert, Jacob Parnell, Jad Kanbar, James E. McDonald, James T. Morton, Jamie M. McDevitt-Irwin, Janet K. Jansson, Jarrad Hampton-Marcell, Jason Andras, Jed A. Fuhrman, Jeff Hooker, Jeffrey J. Werner, Jeffrey Siegel, Jenni Hultman, Jennifer Defazio, Jennifer F. Biddle, Jeremiah Minich, Jesse Zaneveld, Jessica L. Metcalf, Jiří Bárta, Jo Lynn Carroll, John Alverdy, Jon G. Sanders, Jonathan B. Clayton, Jonathan E. Hickman, Jordan Kueneman, Jose A. Navas-Molina, Jose C. Clemente, Jose L. Agosto Rivera, Joseph R. Mendelson, Josephine Braun, Josh D. Neufeld, Joshua Ladau, Joshua Lefler, Jozef I. Nissimov, Juan Diego Ibáñez-Álamo, Juan J. Soler, Juan M. Peralta-Sánchez, Julia K. Baum, Julie D. Jastrow, Julie LaRoche, Karen Noyce, Karen Tait, Karl J. Rockne, Kate Ballantine, Katherine D. McMahon, Katherine R. Amato, Katherine S. Pollard, Kefeng Niu, Kelly D. Goodwin, Kelly Lanede Graaf, Kenneth J. Locey, Kim M. Handley, Kim Miller, Kirsten S. Hofmockel, Krista L. McGuire, Kristin West, Kristina Guyton, L. Margarita Martínez, L. Scott Johnson, Largus T. Angenent, Lauren M. Seyler, Lee J. Kerkhof, Liliana Davalos, Linda A. Whittingham, Lingjing Jiang, Lisa Al-Moosawi, Liza Garcia, Lucas Moitinho-Silva, Lucie Bittner, Lucy Seldin, Ludovic Orlando, Lukas Van Zwieten, Luke K. Ursell, Luke R. Thompson, Magda Magris, Manuel E. Lladser, Manuel Martín-Vivaldi, Manuel Martínez-Bueno, Maria Alexandra Garcia-Amado, Maria Gloria Dominguez-Bello, Mariana Lozada, Mark D. Schrenzel, Martin Sperling, Matthew J. Nolan, Matthew Schrenk, Maureen L. Coleman, Melita A. Stevens, Miguel Lentino, Miles Richardson, Mohamed F. Haroon, Molly K. Gibson, Monica Bhatnagar, Monika Krezalek, Mónica Contreras, Mónica Medina, Naseer Sangwan, Nathalie Fenner, Neslihan Taş, Nicholas A. Bokulich, Nicole M. Scott, Nicole S. Webster, Noah Fierer, Noriko Okamoto, Nur A. Hasan, Olayinka Osuolale, Olivia U. Mason, Pamela Weisenhorn, Paola Piombino, Paola Vitaglione, Paul Munroe, Peter D. Steinberg, Peter Golyshin, Peter Larsen, Peter O. Dunn, Peter Petraitis, Pierre Liancourt, Qikun Zhang, Qiyun Zhu, Rachael M. Morgan-Kiss, Ravi Ranjan, Rebecca J. Safran, Rebecca Vega Thurber, Regina Lamendella, Rick L. Stevens, Rita L. Seger, Rita R. Colwell, Rob Knight, Robert E. Espinoza, Robert G. Clark, Robert J. Prill, Robin B. Gasser, Robin Dowell, Roger Karlsson, Ross Stephen Hall, Russell D. Dawson, Ryan McMinds, Ryan T. Gill, S. Craig Cary, Safiyh Taghavi, Sara Sjöling, Sarah E. Daly, Sarah Jane Haig, Sarah L. O'Brien, Sarah M. Owens, Se Jin Song, Sean M. Gibbons, Selena Marie Rodriguezl, Seth Kauppinen, Shane R. Haydon, Shaun Nielsen, Shi Wang, Siavash Mirarab, Simon Creer, Simon Lax, Sophie Weiss, Stefan Hulth, Stefan Janssen, Stefano Mocali, Stephanie D. Jurburg, Stephen A. Wood, Stephen B. Pointing, Stephen Joseph, Steve Simmons, Steven J. Hallam, Subramanya Rao, Susan R. Whitehead, Suzanne J. Kennedy, Tao Wang, Tim Urich, Tom Weaver, Tomasz Kosciolek, Torsten Thomas, Trevor C. Charles, Tugrul Giray, Ulf Riebesell, Valerie McKenzie, Vanessa Ezenwa, Vanessa Hale, Vera Tai, Vincenzo Fogliano, Virginia Sanz, Walter P. MacCormack, Wayne Roundstone, Wenju Liang, William A. Walters, William Brazelton, William Van Treuren, Wyatt Oswald, Yadira Ortiz Castellano, Yeqin Yang, Yingying Ni, Yongqin Liu, Yoshiki Vázquez-Baeza, Yu Shi, Zhenjiang Zech Xu Nature 2017 718 6
    Universally sloppy parameter sensitivities in systems biology models Christopher R. Myers, Fergal P. Casey, James P. Sethna, Joshua J. Waterfall, Kevin S. Brown, Ryan N. Gutenkunst PLoS Computational Biology 2007 700 6
    Metabolic resource allocation in individual microbes determines ecosystem interactions and spatial dynamics Alex Betts, Alex H. Lang, Amrita Kar, Brian R. Granger, Christopher J. Marx, Daniel Segrè, Gracia Bonilla, Ilija Dukovski, Nicholas Leiby, Pankaj Mehta, William J. Riehl, William R. Harcombe Cell Reports 2014 264 4
    Emergent simplicity in microbial community assembly Alicia Sanchez-Gorostiaga, Alvaro Sanchez, Daniel Segrè, Djordje Bajić, Joshua E. Goldford, Mikhail Tikhonov, Nanxi Lu, Pankaj Mehta, Sylvie Estrela Science 2018 225 11
    Lotka-Volterra pairwise modeling fails to capture diverse pairwise microbial interactions Babak Momeni, Li Xie, Wenying Shou eLife 2017 79 0
    A high-bias low-variance introduction to machine learning for physicists Alexandre G. R. Day, Ching-Hao Wang, Clint Richardson, Pankaj Mehta 2018 0 9 Download
    Available energy fluxes drive a transition in the diversity, stability, and functional structure of microbial communities Alvaro Sanchez, Joshua Goldford, Kirill Korolev, Pankaj Mehta, Robert Marsland III, Wenping Cui PLoS Computational Biology 2019 0 1
    The Minimum Environmental Perturbation Principle: A New Perspective on Niche Theory Pankaj Mehta, Robert Marsland III, Wenping Cui 2019 0 1
    Time and Irreversibility in axiomatic thermodynamics Giovanni Valente, Harvey R. Brown, Robert Marsland III American Journal of Physics 2015 0 0
    Limits of Prediction in thermodynamic systems: a review Jeremy England, Robert Marsland III Reports on Progress in Physics 2017 0 1
    The transition between the niche and neutral regimes in ecology Charles K. Fisher, Pankaj Mehta Proceedings of the National Academy of Sciences 2014 0 2
    Statistical physics of self-replication 0 7

    Samraat Pawar (Imperial College London) - Are changes in species interactions and their ecosystem consequences irreversible?[edit source]

    Temperature-dependence and size scaling of Microbial metabolism

    The question of the temperature-dependence of bacterial metabolism came up in multiple talks. This manuscript from our lab provides some general empirical insights into this:

    '"`UNIQ--nowiki-000008A5-QINU`"'This paper on size-scaling might also be relevant to some: 10.1073/pnas.1007783107

    Natural experiments on effect of temperature on ecosystem structure and function

    Some relevant papers:

    1. Yvon-Durocher, G., Allen, A. & Cellamare, M. Five Years of Experimental Warming Increases the Biodiversity and Productivity of Phytoplankton. PLoS Biol (2015).
    2. Dossena, M. et al. Warming alters community size structure and ecosystem functioning. Proc. R. Soc. B Biol. Sci. 279, 3011–3019 (2012).
    3. Schaum, C.-E. et al. Adaptation of phytoplankton to a decade of experimental warming linked to increased photosynthesis. Nat. Ecol. Evol. 1, 0094 (2017).
    4. Yvon-Durocher, G., Montoya, J. M., Woodward, G., Jones, J. I. & Trimmer, M. Warming increases the proportion of primary production emitted as methane from freshwater mesocosms. Glob. Chang. Biol. 17, 1225–1234 (2011).

    Assembly/Succession/Evolution of microbial/bacterial networks/communities

    1. Lawrence, D. et al. Species interactions alter evolutionary responses to a novel environment. PLoS Biol. 10, e1001330 (2012).

    2. Rivett, D. W. et al. Elevated success of multispecies bacterial invasions impacts community composition during ecological succession. Ecology Letters 21, 516–524 (2018).

    Title Author name Source name Year Citation count From Scopus. Refreshed every 5 days. Page views Related file
    Temperature dependence of trophic interactions are driven by asymmetry of species responses and foraging strategy Anthony I. Dell, Samraat Pawar, Van M. Savage Journal of Animal Ecology 2014 247 0
    Species interactions alter evolutionary responses to a novel environment Diane Lawrence, Francesca Fiegna, Volker Behrends, Jacob G. Bundy, Albert B. Phillimore, Thomas Bell, Timothy G. Barraclough PLoS Biology 2012 217 3
    Five Years of Experimental Warming Increases the Biodiversity and Productivity of Phytoplankton Gabriel Yvon-Durocher, Andrew P. Allen, Maria Cellamare, Matteo Dossena, Kevin J. Gaston, Maria Leitao, José M. Montoya, Daniel C. Reuman, Guy Woodward, Mark Trimmer PLoS Biology 2015 74 0
    Correlation between interaction strengths drives stability in large ecological networks Si Tang, Samraat Pawar, Stefano Allesina Ecology Letters 2014 66 0
    Stressor interaction networks suggest antibiotic resistance co-opted from stress responses to temperature Mauricio Cruz-Loya, Tina Manzhu Kang, Natalie Ann Lozano, Rina Watanabe, Elif Tekin, Robert Damoiseaux, Van M. Savage, Pamela J. Yeh ISME Journal 2018 23 1
    Metabolic traits predict the effects of warming on phytoplankton competition Elvire Bestion, Bernardo García-Carreras, Charlotte Elisa Schaum, Samraat Pawar, Gabriel Yvon-Durocher Ecology Letters 2018 23 1
    Elevated success of multispecies bacterial invasions impacts community composition during ecological succession Damian W. Rivett, Matt L. Jones, Josep Ramoneda, Shorok B. Mombrikotb, Emma Ransome, Thomas Bell Ecology Letters 2018 22 1
    Trophic interaction modifications: an empirical and theoretical framework J. Christopher D. Terry, Rebecca J. Morris, Michael B. Bonsall Ecology Letters 2017 22 0
    The Role of Body Size Variation in Community Assembly Samraat Pawar Advances in Ecological Research 2015 13 0
    Pawar systematic variation 0 4
    Systematic variation in the temperature dependence of physiological and ecological traits Proceedings of the National Academy of Sciences 2011 0 0
    Shifts in metabolic scaling, production, and efficiency across major evolutionary transitions of life Proceedings of the National Academy of Sciences 2010 0 0
    Metabolic traits predict the effects of warming on phytoplankton 0 1

    Stephen Proulx (UCSB) - Population genetics of low-probability transitions[edit source]

    I uploaded a paper by Alan Hastings and others on transient phenomena in ecology, published in Science as a review article.

    I uploaded my paper on the stochastic lottery model that shows transitions between two different population states "What can Invasion Analyses Tell us about Evolution under Stochasticity in Finite Populations?". This paper develops an adaptive dynamics model for evolution of phenotype under a fecundity-survivorship trade off.

    I posted a paper "Indirect genetic effects clarify how traits can evolve even when fitness does not" that relates to some of the discussion about interactions between individuals and the regulating factors that cause feedbacks and may themselves be evolving populations.

    Title Author name Source name Year Citation count From Scopus. Refreshed every 5 days. Page views Related file
    Transient phenomena in ecology Alan Hastings, Karen C. Abbott, Kim Cuddington, Tessa Francis, Gabriel Gellner, Ying Cheng Lai, Andrew Morozov, Sergei Petrovskii, Katherine Scranton, Mary Lou Zeeman Science 2018 128 2
    Indirect genetic effects clarify how traits can evolve even when fitness does not 1930 0 4
    What can Invasion Analyses Tell us about Evolution under Stochasticity in Finite Populations ? Selection 2001 0 0
    Reference Materials by Non-presenting Attendees

    General Meeting Reference Material[edit source]